Principles and psychophysics of Active Inference in anticipating a dynamic probabilistic bias

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain, 5/4/2018

Acknowledgements:

  • Jim Bednar @ Continuum Analytics & University of Edinburgh
  • Berk Mirza, Rick Adams and Karl Friston @ UCL - Wellcome Trust Centre for Neuroimaging
  • Wahiba Taouali, Giacomo Benvenuti, Frédéric Chavane - ANR BalaV1
  • Jean-Bernard Damasse, Laurent Madelain - ANR REM


http://invibe.net/LaurentPerrinet/Presentations/2018-04-05_BCP_talk

Principles and psychophysics of Active Inference in anticipating a dynamic probabilistic bias

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain, 5/4/2018

Acknowledgements:

  • Jim Bednar @ Continuum Analytics & University of Edinburgh
  • Berk Mirza, Rick Adams and Karl Friston @ UCL - Wellcome Trust Centre for Neuroimaging
  • Wahiba Taouali, Giacomo Benvenuti, Frédéric Chavane - ANR BalaV1
  • Jean-Bernard Damasse, Laurent Madelain - ANR REM

Outline

  1. Motivation

  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Motivation - a Real-life example

Motivation - a Real-life example

Motivation - Eye Movements

Montagnini A, Souto D, and Masson GS (2010) J Vis (VSS Abstracts) 10(7):554,
Montagnini A, Perrinet L, and Masson GS (2015) BICV book chapter

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Random-length block design

Motivation - Random-length block design

Outline

  1. Motivation
  2. Raw psychophysical results

  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Raw psychophysical results - Random-length block design

full code @ github.com/chloepasturel/AnticipatorySPEM

Raw psychophysical results

Raw psychophysical results - Fitting eye movements

Raw psychophysical results - Fitting eye movements

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Outline

  1. Motivation
  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector

  4. Results using the BCP

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

Initialize $P(r_0=0)=1$ and $ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$

The Bayesian Changepoint Detector

Observe New Datum $x_t$ and Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) \cdot P (r_t|x_{1:t})$

The Bayesian Changepoint Detector

Evaluate Predictive Probability $π_{1:t} = P(x_t |ν^{(r)}_t,χ^{(r)}_t)$
Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot (1−H(r^{(r)}_{t-1}))$
Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot H(r^{(r)}_{t-1})$

The Bayesian Changepoint Detector

Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $

The Bayesian Changepoint Detector

Update Sufficient Statistics : $ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$
$ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$

Bayesian Changepoint Detector

  1. Initialize
    • $P(r_0)= S(r)$ or $P(r_0=0)=1$ and
    • $ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$
  2. Observe New Datum $x_t$
  3. Evaluate Predictive Probability $π_{1:t} = P(x_t |ν^{(r)}_t,χ^{(r)}_t)$
  4. Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot (1−H(r^{(r)}_{t-1}))$
  5. Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot H(r^{(r)}_{t-1})$
  6. Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
  7. Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
  8. Update Sufficient Statistics :
    • $ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
    • $ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$
  9. Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) \cdot P (r_t|x_{1:t})$
  10. go to (2)

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

Outline

  1. Motivation
  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Results using the BCP - inference with BCP

Results using the BCP - inference with BCP

Results using the BCP - inference with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Principles and psychophysics of Active Inference in anticipating a dynamic probabilistic bias

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain, 5/4/2018

Acknowledgements:

  • Jim Bednar @ Continuum Analytics & University of Edinburgh
  • Berk Mirza, Rick Adams and Karl Friston @ UCL - Wellcome Trust Centre for Neuroimaging
  • Wahiba Taouali, Giacomo Benvenuti, Frédéric Chavane - ANR BalaV1
  • Jean-Bernard Damasse, Laurent Madelain - ANR REM